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Elliptic, parabolic and hyperbolic operators. Laplace, Laplace-Beltrami, Schrödinger, Dirac. Exterior derivative and Lie derivative operators.

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The "Rolle theorem" for sections of a vector bundle

As a first observation, if $(E,\nabla)$ has this Rolle property then if $i: S^1 \to M$ is any embbeding, $(i^*E,i^*\nabla)$ has this property as well (this is just a tubular neighborhood + cutoff argu …
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